We calculate the branching ratios of the K⁺ → π⁰l⁺ν_lγ (l = e, μ) decays, and the T-odd triple momenta correlations ξ = q · [p_l × p_π]/M_K ³, due to the electromagnetic final-state interaction, in these processes. The contributions on the order of ω^-1 and ω⁰ to the corresponding amplitudes are treated exactly. For the branching ratios, the corrections on the order of ω are estimated and demonstrated to be small. We compare the results with those of other authors. In some cases our results differ considerably from the previous ones.